Bottom Line Up Front: I use the Fibonnaci sequence to determine sets, reps, and time when programming exercise training routines. Here is what the Fibonnaci sequence is and how to use it in your training.
What is the Fibonacci Sequence?
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. Mathematically, it’s defined by the formula F(n) = F(n-1) + F(n-2), where F(0) = 0 and F(1) = 1. The sequence typically begins like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. For example, after starting with 0 and 1, the next number is 1 (0+1), then 2 (1+1), then 3 (1+2), and 5 (2+3), showcasing how each subsequent number is formed by adding the two previous numbers in the sequence. This pattern appears in various aspects of nature, art, and mathematics, making it not only a mathematical curiosity but also a recurring theme in understanding growth patterns and structures.
The increase in Fibonnaci numbers from one to the next is always about 1.61, which is the Golden Ratio. In other words, going from 3 to 5 is about a 60% increase. So is 5 to 8. So is 8 to 13. And guess what? So is 13 to 21 and 21 to 34, etc. Going the other way, it’s always 60% less to go from 5 to 3 or from 13 to 8.
I first heard about it learning how to technical analysis on stock charts and still use it today for that purpose. There is a lot here to explore if you are interested in stock, bonds, currency, crypto, etc. Search for “Fibonnaci levels stock charts technical analysis” and get after it. So there I was using Fibonnaci all the time in one area of my life but not applying it to other areas. One day I started using Fibonnaci numbers in my strength training to determine sets and reps for some reason. It morphed from there to now I basically always use it for anything I quantify in my training or for routines I program for others. Sometimes I don’t use it only because it generates a lot of questions because the numbers are somewhat weird without explanation. Imagine you got a routine from me and it had sets of 5 or 8. That would make sense as those are fairly standard. But what about sets of 13 or 21? Or what about 34 minutes of running? 55 minutes of rucking? It’s more “normal” or traditional to have those be sets of 12, 20, 30 or 60 minutes. I will use it more now that I can direct my clients to this article to explain it.
Why and How Do I Use it?
The idea behind is effectively two-fold: 1) It makes all increases and decreases in numbers relative and 2) It gives a clear differentiation between numbers.
I was always bothered by taking absolute changes and applying them broadly. For example, every week, add 10 pounds to your squat. This is an absolute change. If you are squatting 100 pounds, 10 represents 10%. If you are squatting 300, then it’s only 3%. If two people both followed this recommendation, there would be a significant difference in the relative effects of that 10 pounds. The 100-pound squatter had basically three times the increase week-on-week as compared to the 300-pound squatter. So to make it relative, you should use a percentage increase always.
So now let’s look at normal prescriptions for repetition range for someone training for both strength and hypertrophy. We can use repetitions from 1 to 30 to achieve different effects. Let’s say, for example, I started out with 3 sets of 8 reps as a baseline for an exercise, which is fair reasonable for a mix of strength effects and hypertrophy effects. Why not 7 reps? Why not 9? Is 10 better? If 10 is better, is 12 even more better? Again, I am bothered by the absolute increases being different as rep ranges go up. Going from 3 x 5 to 3 x 7 is an increase of 40% (7 is 2 more than 5. 2 is 40% of 5. Hence, going from 5 to 7 is a 40% increase in volume). That is a lot. However, going from 10 to 12 reps is a 20% increase. This is 50% less volume (2 is 50% of 4) than going from 5 to 7 reps per set.
Lot of math there, but hopefully you see my point that there is no clean way of differentiating 8 reps per sets from 9 reps per set and there is a tendency to treat absolute changes equal although they are relatively different. Fibonnaci fixes this.
You start with 3 sets of 8 as that same baseline again, but this time constrain yourself to just increasing or decreasing using Fibonnaci numbers. You want to go up in volume, you go with 3 sets of 13. This is a 60% increase. 13 reps is clearly different from 8 reps. Want to reduce volume? Go to 3 sets of 5 reps. This is a 60% decrease. Want to go down again? 3 sets of 3 (60% decrease).
Let’s apply this to cardiovascular exercise or to a circuit. Baseline of 20 minutes is pretty standard, i.e. conventional wisdom is you have to have your heart rate increased for about 20 minutes to a certain intensity to have any effects on improving parameters of cardiovascular fitness. There is a lot to unpack there and caveat, but, for the sake of example, let’s not argue. Since 20 is close to the Fibonnaci number of 21, let’s start there. 21 minutes of running at a moderate intensity. Want to increase it? We aren’t going to 24 or 28 or 30. We are going to 34, the next Fibonnaci number. Want to decrease it? 13 minutes. Again, this eliminates the question of “What is the difference between 20 minutes and 25?” It seems like it’s the same. And if it’s the same, why are we changing it?
I apply this to calories on cardio machines. Lately I have been doing rounds of multiple cardio pieces for a calorie total then moving to the next machine. Something like: 8-calorie row, 8-calorie run, 8-calorie cycle, then 13-calorie row, 13-calorie run, 13-calorie cycle, then 21 each then 34 each. Each round is a 60% increase from one to the next.
I definitely see another side to this. Sometimes just making it simple, i.e. add 5 pounds per workout or per week or go up one rep makes sense. It may be too much to jump from 21 minutes to 34 minutes of jogging for some people. Using round numbers that are multiples of 2 or 5 are also easy. 20 minutes, then 25 then 30 makes sense too. An absolute increase of 5 minutes may give the desired effects.
For me, Fibonnaci makes a lot of sense for the reasons I’ve outlined. So now you know why you maybe see abnormal sets, reps, and times in articles on this site. Give it a try and see if it’s for you, whether in whole or in part.
Post thoughts to comments below.